document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=93182>Question 93182</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1)Given the binary operation * defined over the set of real numbers R by a*b=a+b+ab. What are the invertible elements of R with respect to *.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #67810 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=67810\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1)Given the binary operation * defined over the set of real numbers R by a*b=a+b+ab. What are the invertible elements of R with respect to *.\r<BR>\n" );
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document.write( "LET I BE THE IDENTITY ELEMENT WRT * OPERATION.SO<BR>\n" );
document.write( "A*I=A=A+I+AI<BR>\n" );
document.write( "I(A+1)=0<BR>\n" );
document.write( "I=0<BR>\n" );
document.write( "HENCE IF X IS INVERSE OF A THEN <BR>\n" );
document.write( "A*X=I=0=A+X+AX<BR>\n" );
document.write( "X(A+1)= -A<BR>\n" );
document.write( "X=-A/(A+1)<BR>\n" );
document.write( "HENCE A SHOULD NOT BE -1<BR>\n" );
document.write( "SO ALL ELEMENTS IN R EXCEPT A=-1 ARE INVERTIBLE </SPAN>\n" );
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